JB: Reuben, sounds like you're about to push some political agenda here, and it's not the
Republican platform.

HERSH: You're saying my philosophy may be biased by my politics. Well, it's true! This is
one of the many novel things in my book-- looking into the correlation between political
belief and belief about the nature of mathematics.

JB: Do you have a name for this solution?

HERSH: I call it humanistic philosophy of mathematics. It's not really a school; no one
else has jumped on the bandwagon with that name, but there are other people who think in
a similar way, who gave it different names. I'm not completely a lone wolf here, I'm one of
the mavericks, as we call them. The wolves baying outside the corral of philosophy.

Anyhow, back to your other question. The second half of my book is about the history of
the philosophy of mathematics. I found that this was best explained by separating
philosophers of mathematics into two groups. One group I call Mainstream and the other I
call Humanists and Mavericks. The Humanists and Mavericks see mathematics as a human
activity, and the Mainstream see it as inhuman or superhuman. By the way, there have
been humanists way back; Aristotle was one. I wondered whether there was any
connection with politics. So I tried to classify each of these guys as either right-wing or
left-wing, in relation to their own times. Plato was far right; Aristotle was somewhat
liberal. Spinoza was a revolutionary; Descartes was a royalist, and so on. These are well
known facts. There are some guys that you can't classify. It came out just as you are
intimating, The humanists are predominantly left-wing and the mainstream predominantly
right wing. Any explanation would be speculative, but intuitively it makes sense. For
instance, one main version of mainstream philosophy of mathematics is Platonism. It says
that all mathematical objects, entities, or whatever, including the ones we haven't
discovered yet and the ones we never will discover-all of have always existed. There's no
change in the realm of mathematics. We discover things, so our knowledge increases, but
the actual mathematical universe is completely static. Always was, always will be. Well
that's kind of conservative, you know? Fits in with someone who thinks that social
institutions mustn't change.

So this parallel exists. But there are exceptions. For instance, Bertrand Russell was a
Platonist and a socialist. One of my favorite philosophers, Imre Lakatos, was a right-
winger politically, but very radical philosophically. These correlations are loose and
statistical, not binding. You can't tell somebody's philosophy from his politics, or vice
versa.

I searched for a suitable label for my ideas. There were several others that had been used
for similar points of view--social constructivism, fallibilism, quasi-empiricism, naturalism. I
didn't want to take anybody else's label, because I was blazing my own trail, and I didn't
want to label myself with someone else's school. The name that would have been most
accurate was social conceptualism. Mathematics consists of concepts, but not individually
held concepts; socially held concepts. Maybe I thought of humanism because I belong to a
group called the Humanistic Mathematics Network. Humanism is appropriate, because it's
saying that math is something human. There's no math without people. Many people think
that ellipses and numbers and so on are there whether or not any people know about them;
I think that's a confusion.